# Multi-Winner Voting with Approval Preferences

arXiv: https://arxiv.org/abs/2007.01795 · HTML: https://mlsanity.com/paper/2007.01795/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 30 of 37)

- [Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback](https://mlsanity.com/paper/2404.10271/) (2024)
- [Generative Social Choice](https://mlsanity.com/paper/2309.01291/) (2023)
- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [Proportional Fairness in Clustering: A Social Choice Perspective](https://mlsanity.com/paper/2310.18162/) (2023)
- [Multiwinner Temporal Voting with Aversion to Change](https://mlsanity.com/paper/2408.11017/) (2024)
- [Generative Social Choice: The Next Generation](https://mlsanity.com/paper/2505.22939/) (2025)
- [Online Approval Committee Elections](https://mlsanity.com/paper/2202.06830/) (2022)
- [Strengthening Proportionality in Temporal Voting](https://mlsanity.com/paper/2505.22513/) (2025)
- [Proportionally Representative Clustering](https://mlsanity.com/paper/2304.13917/) (2023)
- [Not in My Backyard! Temporal Voting Over Public Chores](https://mlsanity.com/paper/2508.08810/) (2025)
- [Method of Equal Shares with Bounded Overspending](https://mlsanity.com/paper/2409.15005/) (2024)
- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [The Leximin Approach for a Sequence of Collective Decisions](https://mlsanity.com/paper/2305.18024/) (2023)
- [Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions](https://mlsanity.com/paper/2306.09835/) (2023)
- [Polynomial-Time Algorithm for Thiele Voting Rules with Voter Interval Preferences](https://mlsanity.com/paper/2604.05953/) (2026)
- [The Complexity of Learning Approval-Based Multiwinner Voting Rules](https://mlsanity.com/paper/2110.00254/) (2021)
- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)
- [A Linear Theory of Multi-Winner Voting](https://mlsanity.com/paper/2503.03082/) (2025)
- [What Voting Rules Actually Do: A Data-Driven Analysis of Multi-Winner Voting](https://mlsanity.com/paper/2508.06454/) (2025)
- [Fair Transit Stop Placement: A Clustering Perspective and Beyond](https://mlsanity.com/paper/2602.06776/) (2026)
- [Computing Thiele Rules on Interval Elections and their Generalizations](https://mlsanity.com/paper/2605.03067/) (2026)
- [On the Complexity of Winner Determination and Strategic Control in Conditional Approval Voting](https://mlsanity.com/paper/2202.01660/) (2022)
- [Most Equitable Voting Rules](https://mlsanity.com/paper/2205.14838/) (2022)
- [Data as Voters: Core Set Selection Using Approval-Based Multi-Winner Voting](https://mlsanity.com/paper/2304.09995/) (2023)
- [Efficient Algorithms for Electing Successive Committees](https://mlsanity.com/paper/2505.18287/) (2025)
- [Algorithmic Shortlisting in Participatory Budgeting](https://mlsanity.com/paper/2508.06577/) (2025)
- [Optimizing Prognostic Biomarker Discovery in Pancreatic Cancer Through Hybrid Ensemble Feature Selection and Multi-Omics Data](https://mlsanity.com/paper/2509.02648/) (2025)
- [Fair Indivisible Payoffs through Shapley Value](https://mlsanity.com/paper/2510.24906/) (2025)

## Abstract (arXiv)

Multi-winner voting is the process of selecting a fixed-size set of representative candidates based on voters' preferences. It occurs in applications ranging from politics (parliamentary elections) to the design of modern computer applications (collaborative filtering, dynamic Q&A platforms, diversifying search results). All these applications share the problem of identifying a representative subset of alternatives -- and the study of multi-winner voting is the principled analysis of this task. This book provides a thorough and in-depth look at multi-winner voting based on approval preferences. One speaks of approval preferences if voters express their preferences by providing a set of candidates they approve. Approval preferences thus separate candidates in approved and disapproved ones, a simple, binary classification. The corresponding multi-winner voting rules are called approval-based committee (ABC) rules. Due to the simplicity of approval preferences, ABC rules are widely suitable for practical use. Recent years have seen a rising interest in ABC voting. While multi-winner voting has been originally a topic studied by economists and political scientists, a significant share of recent progress has occurred in the field of computational social choice. This discipline is situated in the intersection of artificial intelligence, computer science, economics, and (to a lesser degree) political science, combining insights and methods from these distinct fields. The goal of this book is to present fundamental concepts and results for ABC voting and to discuss the recent advances in computational social choice. The main focus is on axiomatic analysis, algorithmic results, and relevant applications.